Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
1150 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 1150 conjugacy classes of subgroups — too many to draw. Only its 171 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#17986394 | C2 | semidirect |
| 3. C2×#17986359 | C2 | semidirect |
| 4. #22587647 | C2 | direct (N × H) |
| 5. C2×#17985738 | C2 | semidirect |
| 6. C2×#329×C71 | C2 | semidirect |
| 12. C2×#14556128 | C22 | semidirect |
| 19. #17986394 | C22 | semidirect |
| 21. #17986359 | C22 | semidirect |
| 24. C2×#14556039 | C22 | semidirect |
| 25. #17985738 | C22 | semidirect |
| 27. C2×#97×C71 | C22 | semidirect |
| 28. #329×C71 | C22 | semidirect |
| 42. #14556128 | C23 | semidirect |
| 64. #14556039 | C23 | semidirect |
| 74. #97×C71 | C23 | semidirect |
| 183. C2×C71 | #1659 | semidirect |
| 192. C2×#329 | D71 | semidirect |
| 193. C71 | C2×#1659 | semidirect |
| 213. C2×#97 | C2×D71 | semidirect |
| 215. #329 | C2×D71 | semidirect |
| 261. #97 | C22×D71 | semidirect |
| 370. C2 | #22587647 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986741 | 2 |
| C2×#17986394 | 2 |
| C2×#17986359 | 2 |
| #22587647 | 2 |
| C2×#17985738 | 2 |
| C2×#329×C71 | 2 |
| C2×#1659 | 71 |